1. a bag contains 12 white counters, 7 black counters and
1 red counter.

a) if, when a counter is taken out, it is not replaced,
calculate the probability that:
i) the first counter is white,

ii) the second counter removed is red, given that the
first was black.

b) if, when a counter is picked, it is then put back in the
bag, how many attempts will be needed before it is
mathematically certain that a red counter will have been
picked out?

Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.